In this article, we shall study the effect of temperature on the value of resistance and thermistors and their uses.

A metallic conductor consists of a large number of free electrons. These electrons are always in a state of random motion. When a potential difference is applied across the ends of the conductor. These free electrons start moving in the definite direction i.e. towards the positive end of the conductor. During this process, the electrons flow through the crowd of vibrating atoms. These electrons collide with the atoms. Thus vibrating atoms offer obstruction to the flow of electrons. This obstruction to the flow of electrons is called the resistance of the conductor.

If the temperature of the conductor is increased, the kinetic energy of vibrating atoms is increased, due to which the atoms start vibrating with higher amplitude. Thus the obstruction to the flow of electrons increases and hence the resistance of the conductor also increases.

Expression for Temperature Coefficient of Resistance:

Let R_o be the initial resistance at 0° C. Let R be the resistance at t° C.

∴ Change in resistance             =    R  –  R_o

∴ Change in temperature (Δt)   =    t₂  – t₁

Experimentally it is found that the change in resistance is directly proportional to

• the original resistance.
• to change in temperature.

R  –  R_o   ∝    R_o       ——— (1)

R  –  R_o   ∝    t₂  – t₁  ——— (2)

From (1) & (2)

R  –  R_o    ∝   R_o  (t₂  – t₁)

R –  R_o    =      α R_o (t₂  – t₁)

Where α is constant called temperature coefficient of resistance.

But    t₂ – t₁ = Δ t

R – R_o    =      α R_o Δ t    ……….. (3)

R   =    R_o + α R_o Δ t

R   =    R_o (1 + α Δ t)

This is an expression which gives the value of resistance at the new temperature.

From equation (3), we have

This is an expression for the temperature coefficient of the resistance of a material of a conductor.

Temperature Coefficient of Resistance:

Temperature coefficient of resistance is defined as the change in resistance per unit resistance at 0° C per degree rise in temperature

Notes:

For good conductors value of temperature coefficient of resistance is positive hence the value of resistance increases as temperature increases and the value of resistance decreases if its temperature decreases

For semiconductors value of temperature coefficient of resistance has a negative value. Hence the value of resistance decreases as temperature increases and the value of resistance decreases if its temperature increases.

Thermistors: 

A thermistor is a special case of a semiconductor having a large negative temperature coefficient of resistance. Thermistors are also called as temperature-sensitive resistance. As they have a large negative value of alpha the value of resistance decreases very fast, as the temperature increases. Thermistors are very sensitive.

Thermistors are made up of oxides of copper, manganese, nickel, cobalt, iron, lithium, etc. These oxides are mixed and are powdered. After this, they are given the desired shape and are heated to very high temperatures. Thus ceramic thermistors are formed. Thermistors are used in the temperature controlling devices or as temperature sensors.

Previous Topic: Introduction to Current Electricity

Next Topic: Kirchhoff’s Laws of Current Electricity

Science > Physics > Current Electricity > Temperature Dependence of Resistance

The post Temperature Dependence of Resistance appeared first on The Fact Factor.

In this article, we shall study the concept of current electricity, the resistance, ohm’s law, and the conductance of a conductor.

Electric Current Through Conductor:

A conductor is made up of very minute particles called atoms. Atoms consist of a positively charged nucleus and negatively charged electrons which move around the nucleus in different orbits. The electrons in the last orbit are loosely attached to the atoms. They can be removed by applying an external force, hence such electrons are called free electrons.

If one end of the conductor is connected to positive terminal of a battery and another end is connected to negative terminal of a battery, negatively charged free electrons start moving towards the positive terminal of battery Thus there is a flow of electron through the conductor and we can say that electric current is flowing through the conductor.

Actually, electrons flow from the negative terminal of a battery to the positive terminal of a battery through the external circuit. But conventionally it is assumed that electric current flows from positive terminal to the negative terminal of a battery.

If ‘e’ is a charge on one electron and ‘Q’ is a total charge flowing through the conductor, then t6he number of electrons (n) flowing through the conductor can be found by using the relation

Q = n e.

Types of Material:

Conductors:

The substances which allow an electric current to flow through them easily are called good conductors of electricity. In conductor electric current flows due to free electrons. e.g. All metals. Silver, Aluminium, Copper, etc.

Insulators:

The substances which do not allow the electric current to flow through them are called bad conductors or insulators of electricity. e.g. Plastic, Rubber, Glass, etc.

Rubber plastic, wood don’t have the free electrons in them, hence they do not allow the electric current to pass through them. Such materials are called as insulators or bad conductors.

Electric Current:

The rate of flow of charge with respect to time through a given cross-section of the conductor is called an electric current. The symbol of the current is ‘I’. The unit of current is ampere (A)

I = q/t

Where I    =   electric current

t    =   time, q   =   electric charge

Potential Difference:

A conductor contains free electrons, which are in random motion i.e. they move in any possible direction with any possible velocity. Due to which the number of electrons passing in unit time through any section of the conductor in one direction is equal to the number of electrons passing in unit time through that section in the opposite direction. Therefore, the net flow of change is equal to zero. Therefore, no current flows through the conductor.

When a potential difference is applied across the conductor the negatively charged electrons start moving towards the positive end of the conductor. Thus electrons start moving in a definite direction. Thus current flows through the conductor. Hence we can conclude that for a flow of electrons in a conductor, the potential difference across the end of the conductor is required.

Cause of a Resistance of a Conductor:

A metallic conductor consists of a large number of free electrons. These electrons are always in a state of random motion. When a potential difference is applied across the ends of the conductor. These free electrons start moving in the definite direction i.e. towards the positive end of the conductor. During this process, the electrons flow through the crowd of vibrating atoms. These electrons collide with the atoms. Thus vibrating atoms offer obstruction to the flow of electrons. This obstruction to the flow of electrons is called the resistance of the conductor.

If the temperature of the conductor is increased, the kinetic energy of vibrating atoms is increased, due to which the atoms start vibrating with higher amplitude. Thus the obstruction to the flow of electrons increases and hence the resistance of the conductor also increases.

Resistance of Wire:

Experimentally it is found that the value of resistance (R) depends on length (L) of a conductor, area of cross-section (A) of conductor and nature of a conductor as follows :

The resistance is directly proportional to the length of a conductor.

R ∝  L   …………..  (1)

The resistance is inversely proportional to the area of a cross-section.

R ∝  1/A   …………..  (2)

The resistance depends on the nature of the conductor.

From equation (1) & (2)

ρ is a constant called specific resistance or resistivity.

This is an expression for the resistance of a conducting wire

This is an expression for the specific resistance or the resistivity of a material of a conductor.

Resistivity or Specific Resistance:

We have,

Let A = 1 unit  and L = 1 unit

∴ R    = ρ

Thus specific resistance or resistivity of a material of a conductor is defined as that resistance of a conductor whose area of cross-section and its length is unity.

Unit of Resistivity:

Therefore, the unit of resistivity or coefficient of resistance is  ohm metre (Ωm)

Conductance:

Reciprocal of resistance is called conductance (K). Its unit is mho or siemens (S).

K = 1 / R

Conductivity:

Reciprocal of resistivity is called conductivity (k). Its S.I. unit is siemens per metre (S/m)

k = 1/ρ

Notes:

• Resistivity is a measure of opposition to the flow of electric current, while conductivity is a measure of assistance to the flow of electric current i.e. easiness of flow of electric current.
• A material exhibiting high resistivity has low conductivity, while material exhibiting high resistivity has low conductivity.

Copper wires are generally used as connecting leads in an electrical circuit.

Copper has an extremely small specific resistance, hence the resistance of a conductor made up of copper is very less. Thus there is a very small loss of electrical energy when a current flows through a copper wire. Due to its high conductivity, a thin copper wire can be used. Hence, copper wires are used to save energy and cost.

Coils of electric iron are made up of nichrome.

Electric-iron works on the principle of the heating effect of electric current. Hence in electric iron more heat is to be produced. When the value of resistance of the coil is more, the more heat is generated. Nichrome is an alloy whose specific resistivity is very high. Hence resistance or coil made from nichrome possesses higher resistance. Hence coils of electric iron are made up of nichrome.

The resistance coils in high-quality resistance boxes are made of manganin.

A resistance box is used in electrical experiments. The resistance box contains a number of resistances of different values. These values should remain constant even if there is a change in room temperature. Manganin has a very small temperature coefficient of resistance and therefore for a small change in temperature, the change in the resistance of a manganin coil is negligible. Hence the value of resistance made from manganin remains constant. Hence the resistance coils in high-quality resistance boxes are made of manganin.

Ohm’s Law:

Statement: 

Physical conditions of the conductor (i.e. the length, area of cross-section, the material, and the temperature) remain the same, the potential difference across the terminal of the conductor is directly proportional to the electric current flowing through the conductor.

Explanation:

Let ‘V’ be the potential difference across the conductor and ‘I’ be the current through it, then by ohm’s law

V ∝   I

V   =   R I

Where R = constant called resistance of the conductor.

Graphical Representation of Ohm’s Law

For conductors obeying ohm’s law, we get a straight line. The resistances obeying ohm’s law are called ohmic resistances or linear resistances.

Note:

For some conductors, we don’t get straight lines but we get curves as shown below.

From the above graphs, we can conclude that these resistances are not obeying ohm’s law that’s why they are called a non- ohmic or non-linear resistance.

Science > Physics > Current Electricity > Introduction

The post Introduction to Current Electricity appeared first on The Fact Factor.

The conductance of an ion depends on its size in an aqueous medium or in the solvent. Bigger is the ionic size lesser is its conductance

Example: The order of size of hydrated ionic radii of alkali metal cations is as Li⁺_(aq) < Na⁺_(aq) < K⁺_(aq)< Rb⁺_(aq)< Cs⁺_(aq). Hence the ease of ionic conductance is Li⁺_(aq) > Na⁺_(aq) > K⁺_(aq) > Rb⁺_(aq) > Cs⁺_(aq)

Concept of Molar Conductivity of an Electrolyte (Λ):

The different solutions may have different concentrations and hence contain a different number of ions. Hence electrolytic conductivity is not a suitable quantity to compare conductance of different solutions. In 1880 the German physicist George Kohlrausch introduced the concept of molar conductivity which is used to compare conductance of different solutions.

The molar conductivity of an electrolyte is defined as the electrolytic conductivity divided by the molar concentration C of the dissolved electrolyte.

Λ = κ / C    or   Λ  = κV

S.I. unit of electrolytic conductivity is siemens per metre (Sm^-1) or S cm^-1. S.I. unit of molar conductivity is siemens square metre per mole (S m² mol^-1). or S cm² mol^-1

If concentration C is measured in M i.e. mol L^-1 or mol dm^-3, then the relationship can be written as

If normality of solution is given then the conductivity is called equivalent conductivity and the relation can be written as

The relation between molar conductivity and equivalent conductivity is

Λ _M =   n Λ_E

Where n is total positive or negative valencies.

Variation of Electrolytic Conductivity with Concentration:

The electrolytic conductivity depends on the number of ions present in a unit volume of a solution. on dilution the degree of dissociation increases. Thus the number of current-carrying ions in the solution increases. But actually, the number of current-carrying ions per unit volume decreases. Hence the activity of the number of ions decreases and hence the electrolytic conductivity also decreases.

For the strong electrolyte, the electrolytic conductivity increases sharply with increasing concentration. For the weak electrolyte, the electrolytic conductivity is very low in dilute solutions and increases much more gradually with increase in the concentration. and this increase is due to an increase in active ions in the solution.

Variation of Molar Conductivity with Concentration:

The molar conductivity of both strong and weak electrolytes increases with dilution i.e. decrease in the concentration.

The molar conductivity is the conductance of all the ions produced by one mole of the electrolyte. Due to an increase in dilution degree of dissociation increases and which results in an increase in the molar conductivity.

For the strong electrolyte, the molar conductivity increases sharply with increasing concentration. Similarly weak electrolyte the molar conductivity increases gradually with an increase in the concentration.

Friedrich Kohlrausch Relation:

Friedrich Kohlrausch performed repeated experiments and plotted a graph of molar conductivity versus the square root of the concentration of a solution.

They showed that the molar conductivity of strong electrolytes varies linearly with the square root of concentration and established the following relation

Where Λ = Molar conductivity at given concentration
Λ_o = Molar conductivity at zero concentration or infinite dilution
C = Concentration of solution
α = constant.

The graph of molar conductivity versus the square root of the concentration of a solution is linear for a strong electrolyte. But such a graph for weak electrolytes is not a straight line.

Kohlrausch Law:

The law states that at infinite dilution, each ion migrates independently of its co-ion and makes its own contribution to the total molar-conductivity of an electrolyte. irrespective of the nature of the other ion with which it is associated.

Thus according to the law at infinite dilution, the total molar conductivity is the algebraic sum of molar conductivities of cation and anion.

Where, Λ = Molar conductivity of a solution
λ ₊^o = Molar conductivity of a cation
λ _–^o = Molar conductivity of an anion

For electrolyte A_mB_n, the molar conductivity at infinite dilution is

Illustration:

In both the cases the difference in of K and Na salt is the difference between Λ_o values of K and Na ions, and it is constant. This illustrates the law.

Applications of Kohlrausch Law:

• The law can be used to calculate the molar-conductivity of any electrolyte at zero concentration.
• The law is particularly useful in the calculation of Λ_o of weak electrolyte for which extrapolation method is not useful.
• Using the extrapolation method value of Λo for strong electrolytes is found and using that value of Λ_o weak electrolyte can be calculated.

Calculation of the Molar Conductivity of any Electrolyte at Zero Concentration:

Let us calculate Λ_o for weak electrolyte acetic acid (CH₃COOH|) using Λ_o values of strong electrolytes sodium acetate (CH₃COONa|) and sodium chloride (NaCl).

The values of  Λ_o for strong electrolytes can be found by extrapolation method and using them for weak electrolyte Λ_o  can be calculated.

Relation Between Molar Conductivity and Dissociation Constant (Theory of Weak Electrolyte) :

Where α = degree of dissociation
Λ = Molar conductivity at concentration C

Λ_o  = Molar conductivity at zero concentration

Now, the dissociation constant k for weak electrolyte is given by

This is the relation between dissociation constant and molar conductivity of the weak electrolyte. This relation is called Ostwald’s equation.

Measurement of Conductivity:

The determination of conductivity and molar conductivity of a solution consists of a measurement of the resistance of the solution using Wheatstone’s metre bridge.

The cell used for measurement consists of a glass tube with two platinum plates coated with a thin layer of finely divided platinum called platinum black. The cell is to be dipped in a solution whose resistance is to be measured as shown in fig.

Now conductivity of a cell is given by

The quantity l/a  is constant and called cell constant and is defined as the ratio of the distance between the electrodes and the area of cross-section of the electrode. It is denoted by ‘b’

The resistance of the solution is found using Wheatstone’s metre bridge. Using the above relation the conductivity of the solution is calculated. The molar conductivity is obtained by using the formula and value of cell constant b can be obtained using the formula b = kR

The circuit arrangement is as shown below.

Types of Conduction:

Metallic Conduction:

The charge transfer through electronic conductors is called metallic conduction

Characteristics of metallic conduction:

• In this conduction, charge transfer occurs through metal.
• It involves the flow of electrons.
• There is no movement of metal atoms.
• There is no chemical change of metal.

Ionic or Electrolytic Conduction:

The charge transfer through electrolytic conductors is called electrolytic conduction

Characteristics of metallic conduction:

• In this conduction, charge transfer occurs through molten electrolyte or its aqueous solution
• It involves the motion of ions in the solution.
• There is a movement of ions.
• There is a chemical change in an electrolyte.

Previous Topic: Introduction to Electrochemistry

Next Topic: Types of Cells

Science > Chemistry > Electrochemistry > Ionic Conduction

The post Ionic Conduction appeared first on The Fact Factor.

In this article, we shall study the concept of electrochemistry, its cause, and its terminology.

Electrochemistry is a branch of chemistry which deals with the interrelationship between chemical energy and electrical energy. The study of electrochemistry is broadly divided into two branches. a) Conversion of chemical energy into electrical energy and b) Conversion of electrical energy into chemical energy. Electrochemistry has wide applications in engineering and science. Michael Faraday is called the father of electrochemistry.

Basic Terminology of Electrochemistry:

Oxidation Reaction:

The loss of an electron or electrons by a species is called oxidation.  Example

Na    →    Na⁺ +    e^–

In oxidation, the oxidation number of elements increases as a result of the loss of electrons. In the above example, the oxidation number of sodium increases from 0 to +1. Thus the oxidation can also be defined as the process in which the oxidation number of an element increase.

Reduction Reaction:

The gain of an electron by a species is called reduction.  Example.

Cl    +     e^–   →     Cl^–

In reduction, the oxidation number of an element decreases as a result of the gain of electrons. In the above example the oxidation number of chlorine decreases from 0 to -1. Thus the reduction can also be defined as the process in which the oxidation number of an element decreases.

Oxidizing Agent (Oxidant):

The substance which accepts electrons and makes the other substance to lose electrons is called oxidizing agent or oxidant. Consider reaction

2Mg     +   O₂    →   2MgO

In this reaction oxygen is making magnesium to lose electrons and hence in this reaction oxygen is the oxidizing agent.

Reducing Agent (Reductant):

The substance which loses electrons and makes the other substance to accept electrons is called a reducing agent or reductant. Consider reaction

2Mg     +   O₂    →   2MgO

In this reaction, magnesium is making oxygen to accept electrons and hence in this reaction magnesium is reducing agent.

Redox Reactions:

In any of a chemical reaction, if one of the reactants is oxidized, the other is surely reduced. Consider reaction

2Mg     +   O₂    →   2MgO

In this reaction, Mg is oxidized to MgO (loss of electrons by Mg), whereas oxygen is reduced to MgO (gain of electrons by oxygen). Hence oxidation and reduction take place simultaneously.  Therefore, all such reactions are called as reduction-oxidation reactions or redox reactions. In all such reactions, one of the reactants loses the electrons (oxidized) while other gains those electrons (reduced). Such a reaction may be expressed as the sum of two half-reactions. One reaction involving loss of electrons by a species and another involving gain of electrons by a species. This is the basis of all electrochemical processes.

Conductance:

The substances that allow the flow of electricity through them are called conductors.  The flow of electricity through a conductor involves the transfer of electrons from one point to the other. Depending on the mechanism of the transfer of electrons, the conductors are classified into two types.  a)  Electronic conductors b) Electrolytic conductors

Electronic Conductors:

The conductors through which the conduction of electricity occurs by direct flow of electrons under the influence of applied potential are known as electronic conductors. e.g. copper, aluminium, silver, mercury etc.

Characteristics of Electronic Conductors:

• In electronic conductors, the flow of electricity occurs by the migration of electrons through the conductor.
• In electronic conductors, the conduction does not involve the transfer of matter.
• In electronic conductors, the conduction process does not involve chemical change.
• The resistance of electronic conductors increases and their conductivity decreases with the increase in temperature.
• Ohm’s law is followed but Faraday’s laws are not followed.

Electrolytic Conductors:

The conductors through which the conduction of electricity occurs by the migration of positive and negative ions under the influence of applied potential are known as electrolytic conductors. e.g. electrolysis of fused NaCl.

Characteristics of Electrolytic Conductors:

• In electronic conductors, the flow of electricity occurs by the migration of positive and negative ions through the conductor.
• In electrolytic conductors, the conduction involves the transfer of matter.
• In electrolytic conductors, the conduction process always involves chemical change.
• The resistance of electronic conductors decreases and their conductivity increases with the increase in temperature.
• Both Ohm’s law and Faraday’s laws are followed.

Resistance and Conductance:

By ohm’s law, V = IR

Where R = Resistance of a conductor V = Potential difference across the conductor I = current through the conductor. S. I. unit of resistance is ohm (Ω), that of potential difference is volt (V) and that of current is ampere (A)

Resistance of an Electronic Conducting Wire:

Experimentally it is found that the value of resistance (R) depends on the length (L) of a conductor, the area of cross-section (A) of conductor and nature of a conductor as follows:-

The resistance is directly proportional to the length of a conductor.

R α  L   ………………. (1)

The resistance is inversely proportional to the area of a cross-section.

R α  1/A   ………………. (2)

The resistance depends on the nature of the conductor.

From equation (1) & (2)

R = ρl / A

This is an expression for the specific resistance or the resistivity of a material of a conductor.

Resistivity or Specific Resistance:

We have, ρ = RA / l

Let A = 1 unit  and L = 1 unit, then ρ = R

Thus specific resistance or resistivity of a material of a conductor is defined as that resistance of a conductor whose area of cross-section and its length is unity.

Unit of Resistivity or Specific Resistance:

We have, ρ = RA / l

Hence unit of ρ  = Unit of R x Unit of Area / Unit of Length = ohm x metre² / metre   = ohm metre

Therefore, S.I. unit of resistivity or specific resistance is ohm metre (Ωm)

Conductance:

Reciprocal of resistance is called conductance (K). Its S.I. unit is mho or siemens.

Conductivity:

Reciprocal of resistivity is called as conductivity (κ)

Conductance of an Electronic Conducting Wire:

Experimentally it is found that 1. The conductance (G) is directly proportional to the area of cross-section (A) of a conductor

G α  A   ………………. (1)

The conductance (G) is inversely proportional to the length (L) of the conductor  

G α  1/L     ………..  (2)

It also depends on the material of the conductor.

From equation (1) & (2)

G α  A / L

G =  κA / L

k is constant called specific conductance or conductivity.

This is an expression for the resistance of a conducting wire.

Now,         Let A = 1 unit  and L = 1 unit , then G = κ

Thus specific conductance or conductivity of a material of a conductor is defined as that conductance of a conductor whose area of cross-section and its length is unity. S.I. unit of conductivity is siemens per metre (S m-1). Other units used are S cm-1, W-1m-1, and W^-1cm^-1.

Next Topic: Ionic Conduction

Science > Chemistry > Electrochemistry > Introduction

The post Introduction to Electrochemistry appeared first on The Fact Factor.